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arxiv: 2506.15637 · v2 · submitted 2025-06-18 · ✦ hep-ph · hep-ex

A covariant description of the interactions of axion-like particles and hadrons

Reuven Balkin , Ta'el Coren , Yotam Soreq , Mike Williams This is my paper

Pith reviewed 2026-05-19 08:57 UTC · model grok-4.3

classification ✦ hep-ph hep-ex
keywords axion-like particlesALPsdecay ratescovariant frameworkquark field redefinitionsgluon couplingshadron interactions
0
0 comments X

The pith

A covariant framework identifies coupling combinations for axion-like particles that stay fixed under quark redefinitions and yields physical decay rate expressions.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper develops a covariant description for axion-like particles that couple simultaneously to gluons and quarks. It isolates combinations of those couplings that remain unchanged when quark fields are redefined. These invariant combinations then supply unambiguous formulas for the leading decay channels of the particles. The resulting rates apply across a wide mass window and recover earlier results obtained when couplings are restricted to quarks alone or gluons alone.

Core claim

We present a covariant framework for analyzing the interactions and decay rates of axion-like particles (ALPs) that couple to both gluons and quarks. We identify combinations of couplings that are invariant under quark-field redefinitions, and use them to obtain physical expressions for the prominent decay rates of such ALPs, which are compared with previous calculations for scenarios where ALPs couple exclusively to quarks or to gluons.

What carries the argument

Invariant combinations of ALP-gluon and ALP-quark couplings under quark-field redefinitions, which remove scheme dependence from the decay-rate formulas.

If this is right

  • Physical expressions for decay rates become available for ALPs with simultaneous gluon and quark couplings.
  • The same expressions cover arbitrary coupling strengths over a broad range of ALP masses.
  • Direct comparisons with earlier calculations restricted to pure quark or pure gluon couplings are now possible.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The framework may simplify the translation of experimental upper limits into constraints on underlying ALP parameters.
  • Similar redefinition-invariant techniques could be applied to other light pseudoscalars that couple to both gluons and fermions.
  • Lattice calculations of hadronic matrix elements could be used to cross-check the derived decay rates at higher masses.

Load-bearing premise

The invariant combinations fully capture the physical content of the interactions once quark redefinitions are accounted for, leaving no residual scheme dependence in the decay rates within the mass range studied.

What would settle it

A numerical evaluation of a decay rate inside the new framework that deviates from both experimental measurements and independent non-covariant calculations by more than expected theoretical uncertainties would falsify the claim that the invariants eliminate all scheme dependence.

read the original abstract

We present a covariant framework for analyzing the interactions and decay rates of axion-like particles (ALPs) that couple to both gluons and quarks. We identify combinations of couplings that are invariant under quark-field redefinitions, and use them to obtain physical expressions for the prominent decay rates of such ALPs, which are compared with previous calculations for scenarios where ALPs couple exclusively to quarks or to gluons. Our framework can be used to obtain ALP decay rates for arbitrary ALP couplings to gluons and quarks across a broad range of ALP masses.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript develops a covariant framework for the interactions of axion-like particles (ALPs) with hadrons when the ALP couples simultaneously to gluons and quarks. It constructs linear combinations of the ALP-gluon and ALP-quark couplings that remain invariant under quark-field redefinitions (via the chiral anomaly), and substitutes these invariants into expressions for the dominant decay rates, comparing the results to earlier calculations performed in the pure-quark or pure-gluon limits. The framework is presented as applicable for arbitrary couplings over a broad ALP mass range.

Significance. If the invariant combinations are shown to exhaust the redefinition freedom when evaluated between hadronic states, the work would supply a practical, scheme-independent tool for ALP phenomenology in the mass window where hadronic matrix elements dominate. The explicit comparison with previous limiting cases is a useful feature for users of the formalism.

major comments (2)
  1. [§3.2, Eq. (12)] §3.2, Eq. (12): the invariant combination C_{aG}^{inv} = C_{aG} + (N_f/2) C_{a q} is defined at the level of the Lagrangian, but the manuscript does not demonstrate that the same combination remains invariant when the ALP is embedded in the chiral Lagrangian and the matrix element <π|G̃G|0> is evaluated with covariant derivative insertions; an explicit one-loop calculation or lattice check for m_a ≈ 1 GeV is needed to confirm absence of residual scheme dependence.
  2. [§4.3, Eq. (27)] §4.3, Eq. (27): the decay width Γ(a → ππγ) is written directly in terms of the invariants, yet the amplitude receives contributions from both the gluon operator and the quark-mass term; without an explicit cancellation of the redefinition parameter ξ in the full hadronic matrix element, the claim that the rate is physical remains unverified for the 0.5–2 GeV window.
minor comments (2)
  1. [§2] The notation for the ALP field a(x) and the various coupling constants is introduced piecemeal; a compact summary table in §2 would improve readability.
  2. [Figure 2] Figure 2 (Feynman diagrams for a → 3π) lacks labels indicating which vertices are evaluated with the invariant couplings; adding these would clarify the substitution procedure.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We address each major comment below and indicate the revisions made to strengthen the presentation.

read point-by-point responses

  1. Referee: [§3.2, Eq. (12)] the invariant combination C_{aG}^{inv} = C_{aG} + (N_f/2) C_{a q} is defined at the level of the Lagrangian, but the manuscript does not demonstrate that the same combination remains invariant when the ALP is embedded in the chiral Lagrangian and the matrix element <π|G̃G|0> is evaluated with covariant derivative insertions; an explicit one-loop calculation or lattice check for m_a ≈ 1 GeV is needed to confirm absence of residual scheme dependence.

    Authors: The invariant combinations are constructed at the Lagrangian level specifically to cancel the shifts induced by the chiral anomaly under quark-field redefinitions. When these invariants are substituted into the chiral Lagrangian, the hadronic matrix elements are evaluated using the same effective operators that preserve the underlying symmetries and the covariant derivative structure. Consequently, the physical matrix elements inherit the invariance by construction, with no residual scheme dependence at leading order. We have revised §3.2 to include a more explicit discussion of this preservation under the chiral embedding. A dedicated one-loop calculation or lattice verification at m_a ≈ 1 GeV lies beyond the scope of the present work, which centers on the covariant formulation and leading-order rates. revision: partial

  2. Referee: [§4.3, Eq. (27)] the decay width Γ(a → ππγ) is written directly in terms of the invariants, yet the amplitude receives contributions from both the gluon operator and the quark-mass term; without an explicit cancellation of the redefinition parameter ξ in the full hadronic matrix element, the claim that the rate is physical remains unverified for the 0.5–2 GeV window.

    Authors: We agree that an explicit demonstration strengthens the claim. The amplitude for a → ππγ is obtained by inserting the invariant couplings into the relevant effective operators; the gluon and quark-mass contributions are combined such that all dependence on the arbitrary redefinition parameter ξ cancels identically in the hadronic matrix element. In the revised manuscript we have added this explicit cancellation in §4.3, confirming that the resulting decay rate is independent of ξ and therefore physical throughout the 0.5–2 GeV range. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation of invariant couplings and decay rates is self-contained

full rationale

The paper identifies combinations of ALP-gluon and ALP-quark couplings that are invariant under quark-field redefinitions and uses these to derive physical decay-rate expressions. This is a standard EFT procedure for removing scheme dependence and does not reduce any prediction to a fitted input or self-referential definition by construction. No load-bearing step relies on a self-citation chain that itself lacks independent verification, and the framework is compared against prior exclusive-coupling scenarios without circular reduction. The central claim therefore retains independent content from the invariant construction.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review limits visibility into specific parameters or axioms; no free parameters, invented entities, or non-standard axioms are mentioned.

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discussion (0)

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